Problem: Takahashi loves sorting.

He has a permutation (p_1,p_2,...,p_N) of the integers from 1 through N. Now, he will repeat the following operation until the permutation becomes (1,2,...,N):

* First, we will define high and low elements in the permutation, as follows. The i-th element in the permutation is high if the maximum element between the 1-st and i-th elements, inclusive, is the i-th element itself, and otherwise the i-th element is low.
* Then, let a_1,a_2,...,a_k be the values of the high elements, and b_1,b_2,...,b_{N-k} be the values of the low elements in the current permutation, in the order they appear in it.
* Lastly, rearrange the permutation into (b_1,b_2,...,b_{N-k},a_1,a_2,...,a_k).



How many operations are necessary until the permutation is sorted?

Constraints

* 1 ≤ N ≤ 2×10^5
* (p_1,p_2,...,p_N) is a permutation of the integers from 1 through N.

Input

Input is given from Standard Input in the following format:


N
p_1 p_2 ... p_N


Output

Print the number of operations that are necessary until the permutation is sorted.

Examples

Input

5
3 5 1 2 4


Output

3


Input

5
5 4 3 2 1


Output

4


Input

10
2 10 5 7 3 6 4 9 8 1


Output

6

Solution (in CPP):

Solution:
#include<stdio.h>
#include<iostream>
#include<vector>
#include<algorithm>
#include<string>
#include<string.h>

using namespace std;

#define REP(i,n) for(int i=0, i##_len=(n); i<i##_len; ++i)

int N;
int A[200011];
int R[200011];

int ring(int a, int b, int c) {
    return (a<b) + (b<c) + (c<a);
}

void MAIN() {
    scanf("%d", &N);
    REP (i, N) scanf("%d", A+i), A[i]--;
    REP (i, N) R[A[i]] = i;
    R[N] = N;
    int f = N;
    int ans = 0;
    for (int i=N; i--;) {
	if (ans == 0) {
	    if (R[i] > R[i+1]) {
		ans = 1;
		f = i+1;
	    }
	} else {
	    if (ring(R[f], R[i], R[i+1]) == 1) {
		ans++;
		f = i+1;
	    }
	}
    }
    printf("%d\n", ans);
}

int main() {
    MAIN();
    return 0;
}